Galton’s Experiment Revisited

This is another cross-post from the blog of the Good Judgment Project.

One of my cousins, Steve Ulfelder, writes good mystery novels. He left a salaried writer’s job 13 years ago to freelance and make time to pen those books. In March, he posted this announcement on Facebook:

CONTEST! When I began freelancing, I decided to track the movies I saw to remind myself that this was a nice bennie you can’t have when you’re an employee (I like to see early-afternoon matinees in near-empty theaters). I don’t review them or anything; I simply keep a Word file with dates and titles.

Here’s the contest: How many movies have I watched in the theater since January 1, 2001? Type your answer as a comment. Entries close at 8pm tonight, east coast time. Closest guess gets a WOLVERINE BROS. T-shirt and a signed copy of the Conway Sax novel of your choice. The eminently trustworthy Martha Ruch Ulfelder is holding a slip of paper with the correct answer.

I read that post and thought: Now, that’s my bag. I haven’t seen Steve in a while and didn’t have a clear idea of how many movies he’s seen in the past 13 years, but I do know about Francis Galton and that ox at the county fair. Instead of just hazarding a guess of my own, I would give myself a serious shot at outwitting Steve’s Facebook crowd by averaging their guesses.

After a handful of Steve’s friends had submitted answers, I posted the average of them as a comment of my own, then updated it periodically as more guesses came in. I had to leave the house not long before the contest was set to close, so I couldn’t include the last few entrants in my final answer. Still, I had about 40 guesses in my tally at the time and was feeling pretty good about my chances of winning that t-shirt and book.

In the end, 45 entries got posted before Steve’s 8 PM deadline, and my unweighted average wasn’t even close. The histogram below shows the distribution of the crowd’s guesses and the actual answer. Most people guessed fewer than 300 movies, but a couple of extreme values on the high side pulled the average up to 346.  Meanwhile, the correct answer was 607, nearly one standard deviation (286) above that mean. I hadn’t necessarily expected to win, but I was surprised to see that 12 of the 45 guesses—including the winner at 600—landed closer to the truth than the average did.

I read the results of my impromptu experiment as a reminder that crowds are often smart, but they aren’t magically clairvoyant. Retellings of Galton’s experiment sometimes make it seem like even pools of poorly informed guessers will automatically produce an accurate estimate, but, apparently, that’s not true.

As I thought about how I might have done better, I got to wondering if there was something about Galton’s crowd that made it particularly powerful for his task. Maybe we should expect a bunch of county fair–goers in nineteenth century England to be good at guessing the weight of farm animals. Still, the replication of Galton’s experiment under various conditions suggests that domain knowledge helps, but it isn’t essential. So maybe this was just an unusually hard problem. Steve has seen an average of nearly one movie in theaters each week for the past 13 years. In my experience, that’s pretty extreme, so even with the hint he dropped in his post about being a frequent moviegoer, it’s easy to see why the crowd would err on the low side. Or maybe this result was just a fluke, and if we could rerun the process with different or larger pools, the average would usually do much better.

Whatever the reason for this particular failure, though, the results of my experiment also got me thinking again about ways we might improve on the unweighted average as a method of gleaning intelligence from crowds. Unweighted averages are a reasonable strategy when we don’t have reliable information about variation in the quality of the individual guesses (see here), but that’s not always the case. For example, if Steve’s wife or kids had posted answers in this contest, it probably would have been wise to give their guesses more weight on the assumption that they knew better than acquaintances or distant relatives like me.

Figuring out smarter ways to aggregate forecasts is also an area of active experimentation for the Good Judgment Project (GJP), and the results so far are encouraging. The project’s core strategy involves discovering who the most accurate forecasters are and leaning more heavily on them. I couldn’t do this in Steve’s single-shot contest, but GJP gets to see forecasters’ track records on large numbers of questions and has been using them to great effect. In the recently-ended Season 3, GJP’s “super forecasters” were grouped into teams and encouraged to collaborate, and this approach has worked quite well. In a paper published this spring, GJP has also shown that they can do well with nonlinear aggregations derived from a simple statistical model that adjusts for systematic bias in forecasters’ judgments. Team GJP’s bias-correction model beats not only the unweighted average but also a number of widely-used and more complex nonlinear algorithms.

Those are just a couple of the possibilities that are already being explored, and I’m sure people will keep coming up with new and occasionally better ones. After all, there’s a lot of money to be made and bragging rights to be claimed in those margins. In the meantime, we can use Steve’s movie-counting contest to remind ourselves that crowds aren’t automatically as clairvoyant as we might hope, so we should keep thinking about ways to do better.

Leave a comment


  1. One important difference Galton’s experiment and subjective forecasting is the set of available information. In the Galton example, everyone has access to identical information (seeing the ox), so measurement + random error is a good model of the cognitive processes involved in guessing the weight, which means that averaging is an accurate aggregation strategy. In forecasting (especially the variety GJP is involved in), the set of available information is dispersed. The situation is more like if each of Galton’s participants saw one cut of an already-butchered ox – maybe a single leg, or a shoulder – and the majority of the animal is not visible to anyone. When people reach the same conclusion based on partial, non-overlapping sets of information, it seems the answer is transform judgments to be more extreme – at least up to the point where one would have gone if one had access to all of the available information.

    Similarly, with Steve, the Facebook friends probably had distinct knowledge of movies that Steve has seen. Maybe you’ve discussed which Christopher Nolan films he’s watched, while someone else knows he was a fan of The Square on Netflix. The individual estimates based on this partial information are not as high as they should be if one had a longer list of some of the movies Steve has seen.

  1. Wisdom of Crowds FTW | Dart-Throwing Chimp

Leave a Comment

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

  • Author

  • Follow me on Twitter

  • Follow Dart-Throwing Chimp on
  • Enter your email address to follow this blog and receive notifications of new posts by email.

    Join 13,609 other subscribers
  • Archives

%d bloggers like this: